What system is used on an engine or cab car to display cab signals and control train speed?

The Train Control Apparatus is utilized on an engine or cab car to both display cab signals and manage train speed. This system integrates various technologies to maintain safe operation by providing real-time information to the engineer regarding speed limits and signal aspects. Additionally, it plays a critical role in ensuring that the train adheres to prescribed speed regulations, significantly enhancing safety.

The other options, while related to train operation, do not specifically encompass both the display of cab signals and the control of train speed in the same way. For instance, a Speedometer System primarily focuses on indicating the current speed of the train but does not provide signal information. The Signal Relay Network involves the communication of signal indications but does not directly manage speed control. An Automatic Braking System is designed to apply the brakes automatically under certain conditions but does not display signals or directly control speed based on them. Therefore, the Train Control Apparatus is the most comprehensive system for the functions described in the question.